Gas Laws

1
Gas Laws

• Charles, Boyle, Gay-Lussac, Combined and The
  Ideal Gas Law

2
The Nature of a Gas

• Gases have mass.
• Its easy to compress gases.
• Gases fill their containers completely.
• Different gases can move through each other quite
  rapidly.
• Gases exert pressure.
• The pressure of a gas depends on its temperature.

3
Kinetic-Molecular Theory

• A gas consists of very small particles, with
  mass.
• The distances between gas particles are
  relatively large.
• Gas particles are in constant, random motion.
• Collisions between gas particles are perfectly
  elastic.
• Average KE of particles depends only on the
  temperature of the gas.
• There is no attractive force between particles of
  a gas.

4
Variables That Effect Gases

• Moles (n) the amount of gas.
• Volume (V) the size of the container that holds
  the gas in liters (L).
• Temperature (T) the speed or kinetic energy of
  the particles in kelvin (oC 273)
• Pressure (P) The outward push of gas particles
  on their container in atmospheres (atm) or
  millimeters of mercury (mm Hg)
• Think of pressure as the number of collisions
  between gas particles and their container.

5
STP

• The behavior of a gas depends on its temperature
  and the pressure at which the gas is held.
• So far we have only dealt with gases at STP.
  Standard Temperature and Pressure.
• 273 kelvins and 1 atm.

6
The Gas Laws

• Boyles Law
• Charless Law
• Gay-Lussacs Law
• The Combined Gas Law
• The Ideal Gas Law

7
Boyles Law

• The Pressure-Volume Relationship
• The pressure and volume of a sample of gas at
  constant temperature are inversely proportional
  to each other.
• (As one goes up, the other goes down)
• P1V1 P2V2
• If 3 of the variables are known, the fourth can
  be calculated.

8
Boyles Law

• The gas in a 20.0mL container has a pressure of
  2.77atm. When the gas is transferred to a 34.0mL
  container at the same temperature, what is the
  new pressure of the gas.
• P1V1 P2V2

9
Boyles Law

• So, does it make sense?
• If a set amount of gas is transferred into a
  larger container, would the pressure go up or
  down?
• Would there be more collisions, or fewer
  collisions with the container holding the gas?
• More volume (space) means fewer collisions with
  the container, therefore pressure goes down.
  (From 2.77 atm to 1.63 atm)

10
Charless Law

• The temperature-volume relationship
• At constant pressure, the volume of a fixed
  amount of gas is directly proportional to its
  absolute temperature.

If 3 of the variables are known, the fourth can
be calculated.
11
Charless Law

• What will be the volume of a gas sample at 355K
  if its volume at 273K is 8.57L?

12
Charless Law

• Does it make sense?
• If the temperature of a given quantity of gas is
  increased, what will happen to the volume it
  occupies? (In an elastic container?)
• Gas particles moving faster would have more
  collisions with the container and exert more
  force to enlarge the volume of the elastic
  container.
• In this case, from 8.57L to 11.1L.

13
Gay-Lussacs Law

• The Temperature-Pressure Relationship
• If a volume of a sample of gas remains constant,
  the temperature of a fixed amount of gas is
  directly proportional to its pressure.

• If you know 3 of the variables, you can
  calculate the 4th.

14
Gay-Lussacs Law

• The gas left in a used aerosol can is at a
  pressure of 2.03atm at 25oC. If this can is
  thrown onto a fire, what is the pressure of the
  gas when its temperature reaches 928oC?

15
Gay-Lussacs Law

• Does it make sense?
• If the temperature of a fixed amount of gas goes
  up, the particles will have more collisions.
  More collisions means the pressure will increase.
• In this case, when the temp went up the pressure
  increased from 2.03atm to 8.18atm.

16
The Combined Gas Law

• If more than one variable changes, a different
  equation is needed to analyze the behavior of the
  gas.

• 5 of the variables must be known to calculate
  the 6th.

17
The Combined Gas Law

• The volume of a gas-filled balloon is 30.0L at
  40oC and 1.75atm of pressure. What volume will
  the balloon have at standard temperature and
  pressure?

18
The Combined Gas Law

• Does it make sense?
• You have a fixed volume of gas. The temperature
  decreases which would cause fewer collisions and
  the pressure decreases which causes fewer
  collisions as well. What can you do to volume to
  make the pressure decrease???
• Increase it. More space means fewer collisions.

19
The Ideal Gas Law

• Describes the physical behavior of an ideal gas
  in terms of the pressure, volume, temperature and
  the number of moles of gas.
• Ideal a gas as it is described by the
  kinetic-molecular theory postulates.
• All gases are REAL gases which behave like ideal
  gases only under most ordinary conditions.

20
The Ideal Gas Law

• Only at very low temperatures and very high
  pressures do real gases show significant
  non-ideal behavior.
• We will assume that gases are close to ideal and
  that the ideal gas equation applies.

21
Ideal Gas Equation

• PVnRT
• P-pressure
• V-volume
• n-number of moles of gas
• R-ideal gas constant (universal gas constant)
  0.0821 atm.L/mol.K
• 8.314 kPa . L/mol.K
• 62.396 torr.L/mol.K
• 62.4 mmHg.L/mol.K
• T-temperature

22
Ideal Gas Equation

• What is the volume occupied by 9.45g of C2H2 at
  STP?

First, calculate amount of gas in moles.
23
Ideal Gas Law
24
Ideal Gas Law

• How many moles of a gas at 100oC does it take to
  fill a 1.00L flask to a pressure of 1.5atm?

25
Lifting Power of Gases

• For a gas to be used to inflate lighter-than-air
  craft like balloons and blimps, the gas must have
  a density lower than air.
• The lower the density, the greater the lifting
  power.

26
Lifting Power of Gases

• The density of a gas depends on its pressure,
  temperature and molar mass.
• Each of these variables is part of the ideal gas
  law.
• Therefore, we should be able to adjust each of
  these variables to give low density.

27
Lifting Power of Gases

• However, if the pressure of the gas within a
  balloon or blimp were significantly less than the
  atmospheric pressure, the balloon or blimp would
  be crushed.
• Therefore, only two factors can be manipulated to
  lower the density of a gas molar mass and
  temperature

28
Molar Mass

• Gases with low density can be corrosive,
  combustible, flammable or chemically active in
  some way. These gases would make poor choices to
  fill blimps and balloons.
• Helium, due to its small molar mass and chemical
  inactivity is the primary choice for balloons and
  blimps.

29
Temperature

• Helium is relatively rare and very expensive, so
  hot air is often preferable.
• As the temperature of a gas is increased, the
  particles increase the number of collisions and
  increase the pressure inside the balloon. The
  volume of the balloon increases and becomes less
  dense and rises.
• Hot air does not have the same lifting power as
  helium, but it is much cheaper.

30
Gas Effusion

• The movement of atoms or molecules through a hole
  so tiny that they do not stream through but
  instead pass through one particle at a time.
• Explains why helium balloons deflate slowly over
  a period of a few hours.
• The lower the mass of the gas, the greater the
  speed of its particles.
• Hydrogen effuses faster than helium. Helium
  effuses faster than oxygen.